(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

From the course of Linear Algebra and Analytic Geometry

I need to find the dimension and two different bases of subspace R^{3}generated by vectors (1,2,3), (4,5,6), (7,8,9).

2. Relevant equations

None.

3. The attempt at a solution

I tried

(a,b,c)=α_{1}(1,2,3)+α_{2}(4,5,6)+α_{3}(7,8,9)

which became

a = α_{1}+ 4α_{2}+ 7α_{3}

b = 2α_{1}+ 5α_{2}+ 8α_{3}

c = 3α_{1}+ 6α_{2}+ 9α_{3}

which (by Gaussian elimination) became an undetermined system with free variable α_{3}.

4. The solution given by teacher

dim=2, example of bases={(1,0,-1),(0,1,2)} or {(2,1,0),(-1,0,1)}

I don't want the solution, I just want to understand the mechanics on how to find the bases and the generated subspace. If someone could explain it to me, thank you.

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# Homework Help: Linear Spaces (Vectors)

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